Find a basis for the plane $x-2y+3z=0$ in $R^3$. Then find a basis for the intersection of that plane with the $xy$ plane.
Is there a proper/algebraic way of finding the basis of a plane?
Just by looking at it a basis could be $(2, 1, 0)$ because any multiple of that will give you $0$ when you substitute, but how do I find this without guessing?
would I use the same process when finding the basis of a line?
Any hints on how to figure out the second part of the question?